ECE 340 Lectures 12-15 Optical Absorption; Recombination; Quasi-Fermi levels

1. ECE 340 Lectures 12-15Optical Absorption; Recombination; Quasi-Fermi levels • Today we turn the light ON semiconductors • Before we do, recall that with the lights OFF, the number of “free” carriers in a sample are just given by: 1) Thermal generation: 2) Charge neutrality: [two equations with two unknowns; a little nicer when ND >> NA or NA >> ND] • When we turn light on, we can generate electron-hole pairs (EHPs), depending on the light frequency (energy)

2. What is the condition for light absorption? • Plot intensity of transmitted light vs. incident photon energy: • Assume ħω > EG and sample of thickness L • The intensity of transmitted photons is: • Where α =

3. Plot the absorption coefficient vs. photon energy: • Keep in mind some of the material band gaps: • Once again, semiconductors absorb photons much more efficiently at energies greater than the band gap (ħω > EG)

4. Light absorbed created excess EHPs (excess with respect to what?) • How long do excess EHPs “live” before they recombine? • Direct EHP recombination occurs spontaneously, emitting a photon of energy _____________ • Excess carrier notation: • δn(t) = δp(t) instantaneous excess EHPs at time t • Δn = δn(t=0) initial excess EHPs at time t = 0, right after initial excitation (e.g. light flash)

5. How do excess EHPs decay? • Assume n-type sample (n0 >> p0) so holes are in minority • Will majority carriers (electrons) be disturbed much? • What about minority carriers (holes)? • Excess minority carriers will recombine with already existing majority electrons: • Solution is a simple exponential: • Where the recombination lifetime for excess EHPs is τ • Typical EHP recombination in Si are τSi ~ • Direct recombination δn decay at same rate as δp

6. Ex: p-doped GaAs sample with 1015 cm-3 acceptors. Flash light (on/off) to initially produce Δn = Δp = 1014 EHPs/cm3 at t=0. Recombination lifetime τ = 10 ns. How do p(t) and n(t) evolve with time?

7. Recombination processes (more generally): • Generation processes:

8. Revisit some definitions: • Thermal equilibrium: generation = recombination • Steady-state: all time derivatives (∂/∂t) = 0 • Ex: A sample of Si doped with NA = 1016 cm-3, with recombination lifetime τ = 1 s. It is exposed continuously to light, such that electron-hole pairs are generated throughout the sample at the rate of 1020 per cm3 per second, i.e. the generation rate gop= 1020/cm3/s. a) What are equilibrium n0 and p0 (before light is on)? b) How many extra δn and δp are there with light on?

9. c) What are total carrier concentrations with light on? d) What is the n∙p product?

10. Note: so far, Fermi level (EF) has only been defined in thermal equilibrium, giving us n and p like: • Q: What does Fermi level look like when we have excess carriers (from light) and hence non-equilibrium? • A: • But we like similar (easy) equations so we define quasi-Fermi levels Fn and Fp:

11. Ex: Calculate and draw quasi-Fermi levels from the previous example.

12. Last but not least. We have all these excess carriers with the lights ON. Does the conductivity (resistivity) change? • Remember: σ = q(μnn0 + μpp0) • Often before, with lights off, we could neglect the minority carriers if the sample was doped n- or p-type • But with lights ON, we have extra carriers δn and δp such that n and p are affected: • Photoconductivity = change in conductivity due to excess carriers (EHPs) from lights being turned on: